[Ifeffit] Fit in R and k space

Frenkel, Anatoly frenkel at bnl.gov
Tue Sep 20 10:54:34 CDT 2005


I personally like this argument in favor of r-space fitting over k-space fitting. I am pretty sure it was made by Ed Stern:

R-space allows to think of EXAFS in terms of radial distribution of atomic positions relative to the central atom. Peaks in r-space usually correspond to atomic positions and the regions between the peaks - to the interstitial regions in the structure (of course, there are 1000 counter-examples, but we are talking about some 'average, well behaving' system where a peak is NOT an atomic AXAFS, nor it is caused by a Ramsauer-Townsend resonance, etc., and a valley is NOT a destructive interference between neighboring shells' - AF). We know, on another hand, that FEFF approximation electron charge density as spherical and the potential as muffin tin. This approximation is not as accurate in the interstitial region between the atoms (where potential profile in real systems may be anything but flat) as it is near the atoms. Thus, intuitively, FEFF should do better job fitting 'peaks' in r-space rather than fitting the interstitial. However, the r-factor and chi square do not really care. Technically, if two models give similar r-factors and chi-square, the one that has better fit in the peak region, the other - in the interstitial, one will examine the r-space fit and choose the one that fits peaks better over the one that fits interstititial region better. However, this information, localized in r-space, is distributed in k-space. Thus, if you look at the graph where data and fit are shown together, either in raw unfiltered k-space or in q-space, the misfit is difficult to interpret. It is, however, possible to interpret the misfit in r-space, and that what often helps to refine the model or choose the better one.

Anatoly

Anatoly Frenkel
Department of Physics
Yeshiva University


-----Original Message-----
From: ifeffit-bounces at millenia.cars.aps.anl.gov
[mailto:ifeffit-bounces at millenia.cars.aps.anl.gov]On Behalf Of Michel
Schlegel
Sent: Tuesday, September 20, 2005 9:07 AM
To: Ravel, Bruce; XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] Fit in R and k space


Hello Bruce,

>Although I prefer to think about the EXAFS problem in R space, I don't think
>this is the reason to do the fit in R space.  Regardless of which fitting
>space you use, you are relying on Feff to supply some fraction of all the
>Fourier components in the data.

We could also used reference-derived phase and amplitude function, as in 
the good ol'time ;)

>  The first-shell feff path only has Fourier
>components (or frequencies, if you prefer) corresponding to the first-shell
>portion of chi(R).  Thus that feff path can only fit those frequencies.
>That's true in k-space as well as in R-space

True in R-space, and that's why Athena-Ifeffit are doing such a wonderful 
job at providing windows to fit only selected area of the fourier transform.
Almost true also in q-space.
In k-space... hmmm, well, I would love to see the mathematical 
demonstration of it for a limited k-range and a Feff(k) (eventhoug I agree 
that many people have performed tha fit in k- and R-spaces, and found about 
the same paramters, so it must be verified somehow).

>What's more, I think the problem of non-modelled shells affecting the 
>modelled
>portion of the data exists in R-space just as much as in k-space.  Because of
>sigma^2 and the finite data range, peaks have width.  In R-space, a given
>path is centered at a particular R-value (or, in other words, its
>contribution to the spectrum is dominated by a particular frequency).
>However, the peak has width (it contains frequencies below and above the
>dominant frequency).  Thus longer paths always interfere with shorter paths
>to some extent.

I think the effect of interfering contributions in the Konigsberger and 
Prins. What I noticed, though, is that the fit of closer shells  can affect 
that of the furthest shell because of the "spillof" from the first peak. 
The recciprocal I was not aware of. But I do agree with you on the whole.
However, I think that in the FT case, these interences are limited to the 
nearest shells, whereas in k-space, nothing protects you from shells at, 
say, 2R and 3R (so to speak.

Best regards,

Michel


-- 
Michel Schlegel
Commissariat à l'énergie atomique
CEN de Saclay, DEN/DANS/DPC/SCP/LRSI
Bat 391 - Piece 205B
F91 191 Gif-sur-Yvette Cedex, France
Ph:  +33 (0)1 69 08 93 84
Fax: +33 (0)1 69 08 54 11



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